5edo: Difference between revisions
Wikispaces>aum-milan **Imported revision 8135657 - Original comment: ** |
Wikispaces>hstraub **Imported revision 25656251 - Original comment: ** |
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<h2>IMPORTED REVISION FROM WIKISPACES</h2> | <h2>IMPORTED REVISION FROM WIKISPACES</h2> | ||
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br> | ||
: This revision was by author [[User: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2008-05-31 06:29:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>25656251</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt></tt><br> | ||
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=5 Equal Divisions of the Octave= | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
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[[space/subscribe/ads|Turn ads off - $5/month]] [[image:http://c1.wikicdn.com/i/edit.png width="128" height="37" caption="Edit This Page" link="5edo"]] | |||
=5 Equal Divisions of the Octave: Theory= | |||
==="equal pentatonic"=== | ==="equal pentatonic"=== | ||
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* [[http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3|Herman Miller]]: //[[http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3|Daybreak on Slendro Mountain]]// (2000) | * [[http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3|Herman Miller]]: //[[http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3|Daybreak on Slendro Mountain]]// (2000) | ||
* Paul Rubenstein: various, with electric guitars in 10- and 15-edo | * Paul Rubenstein: various, with electric guitars in 10- and 15-edo | ||
* Aaron K. Johnson: //5tet funk// (2004) | * Aaron K. Johnson: //[[http://www.akjmusic.com/audio/5tet_funk.mp3|5tet funk]]// (2004) | ||
* Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | * Bill Sethares: //5-tet funk// (2004), //Pentacle// (2004) | ||
* X.J.Scott: //Sleeping Through It All// (2004) | * X.J.Scott: //Sleeping Through It All// (2004) | ||
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Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.</pre></div> | Either way, it is hard to wander very far from where you start. However, it has the scale-like feature that there are (barely) enough notes to create melody, in the form of an equal version of pentatonic.</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5 Equal Divisions of the Octave"></a><!-- ws:end:WikiTextHeadingRule:0 -->5 Equal Divisions of the Octave</h1> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>5edo</title></head><body><!-- ws:start:WikiTextTocRule:26:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:26 --><!-- ws:start:WikiTextTocRule:27: --><a href="#x5 Equal Divisions of the Octave: Theory">5 Equal Divisions of the Octave: Theory</a><!-- ws:end:WikiTextTocRule:27 --><!-- ws:start:WikiTextTocRule:28: --><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --> | <a href="#x5-edo in Musicmaking">5-edo in Musicmaking</a><!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --> | ||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x5 Equal Divisions of the Octave--&quot;equal pentatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;equal pentatonic&quot;</h3> | <!-- ws:end:WikiTextTocRule:40 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="x5 Equal Divisions of the Octave: Theory"></a><!-- ws:end:WikiTextHeadingRule:0 -->5 Equal Divisions of the Octave: Theory</h1> | |||
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="x5 Equal Divisions of the Octave: Theory--&quot;equal pentatonic&quot;"></a><!-- ws:end:WikiTextHeadingRule:2 -->&quot;equal pentatonic&quot;</h3> | |||
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5-edo divides the 1200-<a class="wiki_link" href="/cents">cent</a> octave into 5 equal parts, making its smallest interval exactly <a class="wiki_link" href="/240%C2%A2">240¢</a>, or the fifth root of 2.<br /> | 5-edo divides the 1200-<a class="wiki_link" href="/cents">cent</a> octave into 5 equal parts, making its smallest interval exactly <a class="wiki_link" href="/240%C2%A2">240¢</a>, or the fifth root of 2.<br /> | ||
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5-edo is the smallest <a class="wiki_link" href="/edo">edo</a> containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo)<br /> | 5-edo is the smallest <a class="wiki_link" href="/edo">edo</a> containing xenharmonic intervals! (1edo 2edo 3edo 4edo are all subsets of 12edo)<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5 Equal Divisions of the Octave-Intervals in 5-edo"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals in 5-edo</h2> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="x5 Equal Divisions of the Octave: Theory-Intervals in 5-edo"></a><!-- ws:end:WikiTextHeadingRule:4 -->Intervals in 5-edo</h2> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5 Equal Divisions of the Octave-Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="x5 Equal Divisions of the Octave: Theory-Related scales"></a><!-- ws:end:WikiTextHeadingRule:6 -->Related scales</h2> | ||
<ul><li>By its cardinality, 5-edo is related to other <a class="wiki_link" href="/pentatonic">pentatonic</a> scales, and it is especially close in sound to many Indonesian <a class="wiki_link" href="/slendro">slendros</a>.</li><li>Due to the interest around the &quot;fifth&quot; interval size, there are many <a class="wiki_link" href="/nonoctave">nonoctave</a> &quot;stretch sisters&quot; to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many &quot;circle sisters&quot;:<ul><li>Make a chain of five &quot;bigger fifths&quot; (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul><br /> | <ul><li>By its cardinality, 5-edo is related to other <a class="wiki_link" href="/pentatonic">pentatonic</a> scales, and it is especially close in sound to many Indonesian <a class="wiki_link" href="/slendro">slendros</a>.</li><li>Due to the interest around the &quot;fifth&quot; interval size, there are many <a class="wiki_link" href="/nonoctave">nonoctave</a> &quot;stretch sisters&quot; to 5-edo: square root of 4/3, cube root of 3/2, 8th root of 3, etc.</li><li>For the same reason there are many &quot;circle sisters&quot;:<ul><li>Make a chain of five &quot;bigger fifths&quot; (50/33), which makes three octaves 3.227¢ flat. (50/33)^5=7.985099.</li></ul></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5 Equal Divisions of the Octave-As a temperament"></a><!-- ws:end:WikiTextHeadingRule:8 -->As a temperament</h2> | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="x5 Equal Divisions of the Octave: Theory-As a temperament"></a><!-- ws:end:WikiTextHeadingRule:8 -->As a temperament</h2> | ||
If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.<br /> | If 5-edo is regarded as a temperament, which is to say as 5-et, then the most salient fact is that 16/15 is tempered out. This means in 5-et the major third and the fourth, and the minor sixth and the fifth, are not distinguished. This is at the very edge what can sensibly be called temperament, but it does make sense and can be used.<br /> | ||
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<em>How? Show me!</em><br /> | <em>How? Show me!</em><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="x5 Equal Divisions of the Octave: Theory-Cycles, Divisions"></a><!-- ws:end:WikiTextHeadingRule:10 -->Cycles, Divisions</h2> | ||
5 is a prime number -&gt; 5-edo contains no sub-edos. Only simple cycles:<br /> | 5 is a prime number -&gt; 5-edo contains no sub-edos. Only simple cycles:<br /> | ||
Cycle of seconds: 0-1-2-3-4-0<br /> | Cycle of seconds: 0-1-2-3-4-0<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions</strong>, improvisations</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="x5-edo in Musicmaking-Compositions, improvisations"></a><!-- ws:end:WikiTextHeadingRule:16 --><strong>Compositions</strong>, improvisations</h2> | ||
<ul><li>Brian McLaren: various and sundry</li><li><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>Aaron K. Johnson: <em>5tet funk</em> (2004)</li><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li><li>Andrew Heathwaite: <em>Pinta Penta</em> (2004) (rendered in 6 alternative pentatonics as well)</li><li>Hans Straub: <em><a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow">Asîmchômsaia</a></em><!-- ws:start:WikiTextAnchorRule: | <ul><li>Brian McLaren: various and sundry</li><li><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Herman Miller</a>: <em><a class="wiki_link_ext" href="http://home.comcast.net/%7Eteamouse/daybreak-vsc.mp3" rel="nofollow">Daybreak on Slendro Mountain</a></em> (2000)</li><li>Paul Rubenstein: various, with electric guitars in 10- and 15-edo</li><li>Aaron K. Johnson: <em><a class="wiki_link_ext" href="http://www.akjmusic.com/audio/5tet_funk.mp3" rel="nofollow">5tet funk</a></em> (2004)</li><li>Bill Sethares: <em>5-tet funk</em> (2004), <em>Pentacle</em> (2004)</li><li>X.J.Scott: <em>Sleeping Through It All</em> (2004)</li><li>Andrew Heathwaite: <em>Pinta Penta</em> (2004) (rendered in 6 alternative pentatonics as well)</li><li>Hans Straub: <em><a class="wiki_link_ext" href="http://home.datacomm.ch/straub/mamuth/5tet_e.html#asimchomsaia" rel="nofollow">Asîmchômsaia</a></em><!-- ws:start:WikiTextAnchorRule:41:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@asimchomsaia&quot; title=&quot;Anchor: asimchomsaia&quot;/&gt; --><a name="asimchomsaia"></a><!-- ws:end:WikiTextAnchorRule:41 --></li><li><!-- ws:start:WikiTextAnchorRule:42:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@asimchomsaia&quot; title=&quot;Anchor: asimchomsaia&quot;/&gt; --><a name="asimchomsaia"></a><!-- ws:end:WikiTextAnchorRule:42 --><!-- ws:start:WikiTextAnchorRule:43:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@asimchomsaia&quot; title=&quot;Anchor: asimchomsaia&quot;/&gt; --><a name="asimchomsaia"></a><!-- ws:end:WikiTextAnchorRule:43 --><!-- ws:start:WikiTextAnchorRule:44:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@asimchomsaia&quot; title=&quot;Anchor: asimchomsaia&quot;/&gt; --><a name="asimchomsaia"></a><!-- ws:end:WikiTextAnchorRule:44 --><!-- ws:start:WikiTextAnchorRule:45:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@asimchomsaia&quot; title=&quot;Anchor: asimchomsaia&quot;/&gt; --><a name="asimchomsaia"></a><!-- ws:end:WikiTextAnchorRule:45 --></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Notation</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="x5-edo in Musicmaking-Notation"></a><!-- ws:end:WikiTextHeadingRule:18 -->Notation</h2> | ||
<ul><li>via Reinhard's cents notation</li><li>Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul><br /> | <ul><li>via Reinhard's cents notation</li><li>Sagittal: naturals on a five-line staff, with enharmonics (used interchangably) E=F and B=C</li><li>a four-line hybrid treble/bass staff.</li></ul><br /> | ||